A wireless power transmitting device may have control circuitry that supplies drive signals to a coil to produce wireless power signals. The wireless power receiving device may have a coil that receives the transmitted wireless power signals from the wireless power transmitting device. The wireless power receiving device may have a rectifier that rectifies signals received by the coil in the wireless power receiving device and that provides a rectified voltage to a capacitor. A charger in the wireless power receiving device may charge a battery in the device using the rectified voltage. When it is desired to convey information to the wireless power transmitting device, the wireless power transmitting device may cease the transmission of wireless power and the wireless power receiving device may modulate transistors in the rectifier to transmit data to the wireless power transmitting device.